Table lfunc_lfunctions
L-functions
{'Lhash': '2511629748029413054163802214275', 'a10': [211916.55483486154, 367050.2399389362], 'a2': [-16.0, 27.712812921102035], 'a3': [265.1746853903925, 459.29602797725227], 'a4': [-512.0, -886.8100134752651], 'a5': [6622.392338589423, -11470.319998091756], 'a6': [-16971.17986498512, -6.103169294452102e-60], 'a7': [4344.6368971764805, -44254.388180514856], 'a8': [32768.0, 0.0], 'a9': [-52061.72754378725, 90173.55723564757], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.756804527834246, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [16.0, -27.712812921102035]]], [7, [[1.0, 0], [-4344.6368971764805, 44254.388180514856]]]], 'bad_primes': [2, 7], 'central_character': '14.9', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '1314399976851615751323575404826', 'degree': 2, 'euler_factors': [[[1.0, 0], [16.0, -27.712812921102035]], [[1.0, 0], [-265.1746853903925, -459.29602797725227], [-88573.5, 153413.80220420196]], [[1.0, 0], [-6622.392338589423, 11470.319998091756], [-24414062.5, -42286396.66916204]], [[1.0, 0], [-4344.6368971764805, 44254.388180514856]], [[1.0, 0], [268422.0839933691, 464920.6873500359], [-142655835305.5, 247087154745.30405]], [[1.0, 0], [-1107095.632995402, 0], [1792160394037.0, 0]], [[1.0, 0], [-458258.0993708689, -793726.3110902923], [-17135948153816.5, 29680332838276.28]], [[1.0, 0], [1862830.5612007831, -3226517.1778918016], [-58245129449109.5, -100883523499283.9]], [[1.0, 0], [11288204.463826962, -19551743.657574095], [-476404878956963.5, -825157455327161.9]], [[1.0, 0], [108153231.31197608, 0], [12200509765705828, 0]], [[1.0, 0], [-125690687.7400973, -217702657.2041231], [-12704238448202416, 22004386463756576]], [[1.0, 0], [-201779805.12802795, 349492874.4230915], [-88958810889730200, -154081180241924220]], [[1.0, 0], [-1262658382.3869748, 0], [550329031716248450, 0]], [[1.0, 0], [192414955.94814688, 0], [929293739471222700, 0]], [[1.0, 0], [-504901451.57688487, 874514966.9464419], [-1236079607542006300, -2140952682462552600]], [[1.0, 0], [226217860.60699606, 391820828.15085125], [-4634517964686095000, 8027220583427022000]], [[1.0, 0], [-1813674890.841161, -3141377059.3488283], [-15077944222368922000, 26115765466832577000]], [[1.0, 0], [4938482639.204202, -8553702843.398519], [-21756958805717918000, -37684158069686520000]], [[1.0, 0], [-9550578228.948227, -16542086734.199512], [-61065066452484006000, 105767797663272090000]], [[1.0, 0], [-5710078106.654866, 0], [231122292121701580000, 0]], [[1.0, 0], [4818050230.058212, 8345107791.879742], [-156863342784179860000, 271695279547292350000]], [[1.0, 0], [7832782971.56648, -13566778071.413471], [-373996905263760500000, -647781641790357200000]], [[1.0, 0], [-11023014502.83242, 0], [1287831418538085800000, 0]], [[1.0, 0], [-24332983029.800232, 42145962907.32528], [-1387586536883495000000, -2403370381780759600000]], [[1.0, 0], [133855385872.1648, 0], [7153014030880804000000, 0]], [[1.0, 0], [-12624341315.33569, -21866000570.252323], [-5578341733326583000000, 9661971304103478000000]], [[1.0, 0], [43070333199.15553, -74600005399.85797], [-6921169353622228000000, -11987816968262345000000]], [[1.0, 0], [35515027225.351616, -61513831586.50093], [-10524259761499174000000, -18228552618969286000000]], [[1.0, 0], [2353066099.9715285, 4075630038.7186346], [-12902132026527038000000, 22347148195906435000000]], [[1.0, 0], [-69165981279.17876, 0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10831876, 'index': 5, 'label': '2-14-7.2-c11-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/14/12/c/a/9/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 27}, 'plot_values': [1.9762691464791464, 2.0564116728482986, 2.05485710945571, 1.9762364254608715, 1.8284614421884378, 1.6224740464982788, 1.371892385539257, 1.0925534618885087, 0.8019534416056907, 0.5185902310575273, 0.261217534800988, 0.04802559999258495, -0.10422905099185767, -0.1811148001570036, -0.17139899553844024, -0.06785952434658235, 0.13201737628807667, 0.4255078889843305, 0.8043450395883287, 1.2546879637164452, 1.7574085107425927, 2.288723791404637, 2.821184207869964, 3.3250027649813534, 3.769684115696274, 4.12588249781331, 4.3673886884617215, 4.47312001837803, 4.428967327863542, 4.229341545079281, 3.8782631115904245, 3.3898519599768573, 2.7881053947944414, 2.1058959748223063, 1.3831797101798249, 0.6644732279524539, -0.0042680179281097495, -0.5791664372647362, -1.0220668750368367, -1.3039960672837494, -1.4081025378739371, -1.3317517400448229, -1.0874950047710858, -0.7027097158263098, -0.21781879548957778, 0.31686742257702255, 0.8454960372994298, 1.3118664294663984, 1.6650115102167096, 1.8646110588984548, 1.8856438611257833, 1.7217096680999975, 1.3865450921477367, 0.9134171891369665, 0.35229375726811685, -0.2350591699696826, -0.7816413398749714, -1.2227939962067327, -1.5039543288355341, -1.58765806718615, -1.4588703246926835, -1.1278550577085216, -0.6300398302442983, -0.02267521350646844, 0.6215083884069819, 1.2230277130195208, 1.7057660774910093, 2.00722133102341, 2.087494716990315, 1.9356916988540396, 1.5726575946462553, 1.0493996436918183, 0.4411088754416527, -0.16267880600014864, -0.6706384408398008, -1.0032939748899874, -1.1058110275418036, -0.9579863291715035, -0.57973655676608, -0.03092967838341511, 0.5948351365074135, 1.1820050762570984, 1.6090289082475562, 1.7663653939291462, 1.5739468779369743, 0.9953961800336493, 0.04660865522456715, -1.2029731797381533, -2.6370308276936103, -4.10641525791164, -5.448793980903656, -6.511133447483064, -7.171644337115274, -7.35772770421889, -7.056937953986849, -6.318981686605786, -5.2481629114665855, -3.9872504171038465, -2.6952214329717608, -1.5224631464785556, -0.5875702781146183, 0.04026955240027818, 0.3501742865487877, 0.388085176972425, 0.24506887633101798, 0.037446215480370366, -0.11763245512021124, -0.12658085421012225, 0.06098063312002864, 0.4412886086448858, 0.9565958850725071, 1.506709674134851, 1.9699301437176782, 2.229431934462672, 2.1998464842651804, 1.8485104760561024, 1.2066626435578054, 0.36769732727134924, -0.5278939849291692, -1.3185180974585868, -1.853625016365604, -2.0256534659230963, -1.7950947915720432, -1.2030328890210586, -0.3677979476986126, 0.5345099682317065, 1.3025199078713932, 1.7491116534718951, 1.7401655208909734, 1.2244936128854793, 0.24833779330682015, -1.0492746035654978, -2.460186842534354, -3.745649921068423, -4.682300907287802, -5.106273694352078, -4.946180415202457, -4.23774615028805, -3.11656760350365, -1.7900633362546585, -0.4942159657999953, 0.5558305242045094, 1.2106767454974996, 1.4171695226873022, 1.227563037480739, 0.785025898460511, 0.2884653089321269, -0.055596376150381786, -0.0832263797600807, 0.286216920242416, 1.028525698349676, 2.017624742900877, 3.052867730211806, 3.904698488537698, 4.368257707750011, 4.312402106324088, 3.7124257388773447, 2.658424035333252, 1.3369228908941675, -0.010212904575631971, -1.1400162552099409, -1.862882759351709, -2.084114769067301, -1.8224149703603032, -1.200807217050404, -0.4123177084680335, 0.33084842331590764, 0.8515964401593292, 1.051618575063165, 0.9329690060615803, 0.591707254003007, 0.18512694031548768, -0.11875443001587105, -0.1956998556476968, -0.00845467237239607, 0.3741299600574974, 0.7887374380540386, 1.0184940776914135, 0.8534822620052154, 0.15524212457496214, -1.0923820396788717, -2.761056446063885, -4.59261266848358, -6.249331139154822, -7.3890787221070084, -7.747341768854618, -7.205423230462389, -5.8266520345246775, -3.8499322445138504, -1.6405522161890298, 0.39081445063191983, 1.881465691464979, 2.5992586387271106, 2.493595595889271, 1.7017967831556309, 0.5092460184324762, -0.7263038419051531, -1.6664904977184316, -2.0761960714196666, -1.8777379553816913, -1.161740263703202, -0.15285899086188112, 0.8591410546182704, 1.6030638207229906, 1.9010083705749554, 1.7133237216566526, 1.1417766491986951, 0.39115387932003204, -0.29832631720748837, -0.7268937837087234, -0.7961449424732607, -0.5363347438964772, -0.09163104016918079, 0.3321464712325998, 0.5410256562997348, 0.424361116612625, 0.0010714626605828907, -0.5753540987719948, -1.0566475027153672, -1.173963714366772, -0.7248564468873827, 0.3535917150192055, 1.9490607868859127, 3.7888501252033926, 5.503551194856595, 6.722838160420204, 7.176255633077956, 6.7693455345252564, 5.611859328454596, 3.9884932471967245, 2.279609286801319, 0.8546498346021061, -0.03031606187426645, -0.3001393237135199, -0.07257567405129381, 0.38922847688856355, 0.7693675624958525, 0.8082680164187039, 0.3938990782209286, -0.39432234702784774, -1.3041008346001728, -1.9870897832116519, -2.1111967887044, -1.4736980002730025, -0.07919716956389217, 1.8435486802091254, 3.893498743020191, 5.604194571363104, 6.574444361980333, 6.583534943788493, 5.655687489503107, 4.053568130625399, 2.2022814099856354, 0.5666908374124879, -0.4806429940708188, -0.760787620172742, -0.3286905119951987], 'positive_zeros': ['1.98132651661050457366425651786300', '2.70651237357779342933101771980083', '6.32693243609154122973787998787684', '7.80694386158115997859180123284679', '9.597290281683007872127067001488636', '11.08045225881733555912863957245850', '12.78297411073900438835415617317112', '13.89567344869995829010283792251540', '15.12449396870903749565165998469383', '17.73913768162194200180144405716947'], 'prelabel': '2-14-7.2-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2797567787618407, 'root_angle': 0.005488514421482656, 'root_number': '0.9994054391347721 + 0.03447851835322138*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00548851442148', 'prec': 40}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98132651661050457366425651786', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.70651237357779342933101771980', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.32693243609154122973787998788', 'prec': 100}}